The challenge of artificial mathematical intuition has been recognized since the beginning of the field. Just yesterday I found a quotation in the book I'm reading by Matteo Pasquinelli, soon to be reviewed here, from the review of Wiener's "Cybernetics" by Wolfgang Köhler:
"It is not astonishing that, so far as speed is concerned, so far as speed is concerned, the substituted operations of machines are far superior to anything that humans can achieve. At the same time, these operations appear to generically different from those of a human being who is occupied with a mathematical problem... The machines do not know, because among their functions there is none that can be compared with insight into the meaning of a problem."
The full reference: review of Cybernetics or Control and Communication in the Animal and the Machine, by Norbert Wiener, Social Research 18 (1951): 127-28.
Meanwhile, this morning I watched an online broadcast of a lecture by Amaury Hayat at Erlangen. One of his slides reads:
- Al is already useful in the practice of mathematics and has solved several difficult problems.
- Al is trained to have better intuition than humans on a specific problem.
- This augmented intuition altows us to bypass the difficulty of the problem.
Your quotation refers to '' meaning '' of a problem ,but this is a different question,connected with the general agreement that machines do NOT '' understand '' . But my question is different : can machines ask a good - or a meaninful or... - mathematical question ?
The challenge of artificial mathematical intuition has been recognized since the beginning of the field. Just yesterday I found a quotation in the book I'm reading by Matteo Pasquinelli, soon to be reviewed here, from the review of Wiener's "Cybernetics" by Wolfgang Köhler:
"It is not astonishing that, so far as speed is concerned, so far as speed is concerned, the substituted operations of machines are far superior to anything that humans can achieve. At the same time, these operations appear to generically different from those of a human being who is occupied with a mathematical problem... The machines do not know, because among their functions there is none that can be compared with insight into the meaning of a problem."
The full reference: review of Cybernetics or Control and Communication in the Animal and the Machine, by Norbert Wiener, Social Research 18 (1951): 127-28.
Meanwhile, this morning I watched an online broadcast of a lecture by Amaury Hayat at Erlangen. One of his slides reads:
- Al is already useful in the practice of mathematics and has solved several difficult problems.
- Al is trained to have better intuition than humans on a specific problem.
- This augmented intuition altows us to bypass the difficulty of the problem.
Is he using a different definition of intuition?
Your quotation refers to '' meaning '' of a problem ,but this is a different question,connected with the general agreement that machines do NOT '' understand '' . But my question is different : can machines ask a good - or a meaninful or... - mathematical question ?
I do not think Hayat claims the machines in his examples create the question : their '' inuition'' ( ?) helps as assistant to solve the problems.
Also in his claim '' AI is trained to have better ... ona specific problem '' ( raised by humans ! Not by machines.